Modelling and Economic Optimal Control for a Laboratory-scale Continuous Stirred Tank Reactor for Single-cell Protein Production

TL;DR

This paper develops a coupled growth and pH kinetic model for micro-organism cultivation in a lab-scale reactor, ensuring numerical stability and demonstrating economic optimal control with non-trivial input profiles.

Contribution

It introduces a novel kinetic model for micro-organism growth coupled with pH dynamics and a stable simulation method, applied to optimal control in a laboratory reactor.

Findings

Successful simulation of growth and pH dynamics

Identification of non-trivial optimal input profiles

Enhanced numerical stability in model simulation

Abstract

In this paper, we present a novel kinetic growth model for the micro-organism \textit{Methylococcus capsulatus} (Bath) that couples growth and pH. We apply growth kinetics in a model for single-cell protein production in a laboratory-scale continuous stirred tank reactor inspired by a physical laboratory fermentor. The model contains a set of differential algebraic equations describing growth and pH-dynamics in the system. We present a method of simulation that ensures non-negativity in the state and algebraic variables. Additionally, we introduce linear scaling of the algebraic equations and variables for numerical stability in Newton's method. Finally, we conduct a numerical experiment of economic optimal control for single-cell protein production in the laboratory-scale reactor. The numerical experiment shows non-trivial input profiles for biomass growth and pH tracking.